Sally can paint a room in 6 hours while it takes Steve 4 hours to paint the same room. How long would it take them the room if they worked together
1/6 + 1/4 = 1/x
x = 12/5
so it will take them 2hr 24min to do it to gether
To determine how long it would take Sally and Steve to paint the room if they work together, we can use the concept of work rates.
Let's first find their individual work rates:
Sally's work rate = 1 room / 6 hours = 1/6 rooms per hour.
Steve's work rate = 1 room / 4 hours = 1/4 rooms per hour.
Now, when they work together, their work rates simply add up:
Combined work rate = Sally's work rate + Steve's work rate
= 1/6 rooms per hour + 1/4 rooms per hour
= 2/12 rooms per hour + 3/12 rooms per hour
= 5/12 rooms per hour.
This means that Sally and Steve can complete 5/12 of the room in one hour when they work together.
To find out how long it would take them to complete the whole room, we can divide the total work (1 room) by their combined work rate:
Time required = Total work / Combined work rate
= 1 room / (5/12 rooms per hour).
To simplify, we can multiply the numerator and denominator by 12:
Time required = 1 room × (12 / 5 rooms per hour)
= 12 / (5/1) hours
= 12 × 1/5 hours
= 12/5
= 2.4 hours.
Therefore, it would take Sally and Steve approximately 2.4 hours (or 2 hours and 24 minutes) to complete the room if they work together.